<abstract xmlns="http://www.w3.org/1999/xhtml"><p>An inconsistency with respect to variable transformations in our previous treatment of the cosine error example with repositioning (<italic>Metrologia</italic>, vol. 47, pp. R1–R14) is pointed out. The problem refers to the measurement of the vertical height of a column of liquid in a manometer. A systematic effect arises because of the possible deviation of the measurement axis from the vertical, which may be different each time the measurement is taken. A revised procedure for treating this problem is proposed; it consists in straightforward application of Bayesian statistics using a conditional reference prior with partial information. In most practical applications, the numerical differences between the two procedures will be negligible, so the interest of the revised one is mainly of conceptual nature. Nevertheless, similar measurement models may appear in other contexts, for example, in intercomparisons, so the present investigation may serve as a warning to analysts against applying the same methodology we used in our original approach to the present problem.</p></abstract>

An inconsistency with respect to variable transformations in our previous treatment of the cosine error example with repositioning (Metrologia, vol. 47, pp. R1–R14) is pointed out. The problem refers to the measurement of the vertical height of a column of liquid in a manometer. A systematic effect arises because of the possible deviation of the measurement axis from the vertical, which may be different each time the measurement is taken. A revised procedure for treating this problem is proposed; it consists in straightforward application of Bayesian statistics using a conditional reference prior with partial information. In most practical applications, the numerical differences between the two procedures will be negligible, so the interest of the revised one is mainly of conceptual nature. Nevertheless, similar measurement models may appear in other contexts, for example, in intercomparisons, so the present investigation may serve as a warning to analysts against applying the same methodology we used in our original approach to the present problem.

The Cosine Error: A Bayesian Procedure for Treating a Non-repetitive Systematic Effect

Department of Mechanical and Metallurgical Engineering, Pontificia Universidad Católica de Chile, Vicuña Mackenna 4860, Santiago, Chile

Metrolytik, Kernstockstr. 4, 8600 Bruck an der Mur, Austria

Measurement Science Review

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

An inconsistency with respect to variable transformations in our previous treatment of the cosine error example with repositioning (Metrologia, vol. 47, pp....

The Cosine Error: A Bayesian Procedure for Treating a Non-repetitive Systematic Effect

Published Online: Aug 19, 2016

Page range: 211 - 217

Received: Feb 24, 2016

Accepted: Aug 01, 2016

DOI: https://doi.org/10.1515/msr-2016-0026

Keywords
Cosine error, probability density function, Bayesian statistics, reference prior, Borel’s paradox

© 2016 Ignacio Lira et al., published by De Gruyter Open

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

The Cosine Error: A Bayesian Procedure for Treating a Non-repetitive Systematic Effect

Published Online: Aug 19, 2016

Page range: 211 - 217

Received: Feb 24, 2016

Accepted: Aug 01, 2016

DOI: https://doi.org/10.1515/msr-2016-0026

KeywordsCosine error, probability density function, Bayesian statistics, reference prior, Borel’s paradox

© 2016 Ignacio Lira et al., published by De Gruyter Open

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
Cosine error, probability density function, Bayesian statistics, reference prior, Borel’s paradox